1. Let S = {V1, V2, V3} C R³ where V₁ = (1, 0, 0), V₂ = (1,1,0), V3 = = (1, 1, 1). Use the Gram-Schmidt process to • determine an orthonormal basis for the subspace (S) with one of the basis vectors parallel to v₁ • determine an orthonormal basis for (S) with one of the basis vectors par- allel to V₂. • determine an orthonormal basis for (S) with one of the basis vectors par- allel to V3.

1. Let S = {V1, V2, V3} C R³ where V₁ = (1, 0, 0), V₂ = (1,1,0), V3 = = (1, 1, 1). Use the Gram-Schmidt process to • determine an orthonormal basis for the subspace (S) with one of the basis vectors parallel to v₁ • determine an orthonormal basis for (S) with one of the basis vectors par- allel to V₂. • determine an orthonormal basis for (S) with one of the basis vectors par- allel to V3.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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